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The design of a water network requires the selection of pipe diameters that satisfy pressure and flow requirements while optimizing for cost. This work focuses on the design of moderate-scale branching Gravity-Driven Water Networks (GDWNs), in contrast to large urban-scale looping networks, where budgets are highly constrained and where PVC pipe is typically used. In order to help designers of GDWNs select an appropriate design approach for a given network problem, three cost-minimization algorithms are developed and compared on five GDWN test cases. Two algorithms, a backtracking algorithm and a genetic algorithm, use a set of discrete pipe diameters, while a new calculus-based algorithm produces a continuous-diameter solution, which is mapped onto a discrete-diameter solution. The backtracking algorithm produced the overall lowest-cost solutions with relative efficiency for the test cases, while the calculus-based algorithm produced slightly higher-cost results but with greater scalability to networks with more links. Furthermore, the new calculus-based algorithm’s continuous-diameter and mapped solutions provided lower and upper bounds, respectively, on the discrete-diameter global optimum cost, where the mapped solutions were typically within one diameter size of the global optimum. Overall, the genetic algorithm as implemented did not produce results, which deemed it compelling over deterministic methods as applied to GDWNs. However, for more complex networks and problem formulations, a genetic algorithm may be more advantageous, particularly if it incorporates improvements reported in the literature.